Emerging computing paradigms like mist, edge, and fog computing address challenges in the real-time processing of vast Internet of Things (IoT) applications. Alongside, cloud computing offers a suitable platform for executing services. Together, they form a multi-tier computing environment known as compute-continuum to efficiently enhance data management and task execution of real-time tasks. The primary considerations for compute-continuum include variations in resource configuration and network architecture, rental cost model, application security needs, energy consumption, transmission latency, and system reliability. To address these problems, we propose two scheduling algorithms (RCSECH and RSECH) for real-time multi-workflow scheduling frameworks. Both algorithms optimize for rental cost, energy consumption, and task reliability when scheduling real-time workflows while considering deadlines and security requirements as constraints. RCSECH also factors in reliability alongside these constraints. The environment under investigation consists of a compute-continuum architecture consisting of mist, edge, fog, and cloud layers, each potentially composed of heterogeneous resources. The framework undergoes evaluation via simulation experiments, revealing promising results. Specifically, the framework exhibits the capability to enhance reliability by up to 7%, reduce energy consumption by 8%, surpass reliability constraints by more than 25%, and generate cost savings by at least 15%.